Trisha Daigle



Psy 633: One-sample t-test

Generally, the t-test is used in two contexts:

As a sub for z when some of the info for z is unknown

This is the “one-sample” test – not terribly common, but sometimes useful

As a test for comparing two samples when no population info at all is available

This is the most common version – widely used in all sciences.

Problems with z:

Usually don’t know enough about the population to compute z

Especially a problem regarding standard error

Less versatile than t – i.e., can’t be used in as many different situations

Can be used when µ is known, but σ is not known

Can be used when µ is not known, but can be reasonably estimated or else

arbitrarily established: e.g., as in manufacturing and education, where an

“ideal” mean can be stipulated

Solution: substitute sample std error for pop std error in the z formula

This new formula is the t-test formula

In the single-sample test, one degree of freedom is lost to the sample mean, so the test has n-1 degrees of freedom [df = the # of scores that are free to vary, taking into account the computation of the mean]

As df increases, sample var is better estimator of pop var

also t is better approximation of z (distribution approaches normal)

Weakness of t is that there is more variability in it, thus more chance of making a Type I decision error

Solution is to use as large an n as feasible

In formula,

Numerator reflects: effect of the IV on the DV

[Note that this is one of the major “power” factors]

Denominator reflects:

Individual diff’s, n, unwanted var (“error”)

[Note that all of these are major “power” factors]

The problem for the researcher is to make the numerator as large as possible, within ethical & practical reason, and the denominator as small as possible. Assuming that both of those ends are accomplished, then if there is a diff betw M and µ, the t-test will reveal it.

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